/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    Eclipse Public License Version 1.0.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

/*
$begin rev_sparse_hes.cpp$$
$spell
	Hessian
	Jac
	Hes
	Dep
	Cpp
$$

$section Reverse Mode Hessian Sparsity: Example and Test$$
$mindex RevSparseHes sparsity$$


$code
$srcfile%example/sparse/rev_sparse_hes.cpp%0%// BEGIN C++%// END C++%1%$$
$$

$end
*/
// BEGIN C++

# include <cppad/cppad.hpp>
namespace { // -------------------------------------------------------------

// expected sparsity pattern
bool check_f0[] = {
	false, false, false,  // partials w.r.t x0 and (x0, x1, x2)
	false, false, false,  // partials w.r.t x1 and (x0, x1, x2)
	false, false, true    // partials w.r.t x2 and (x0, x1, x2)
};
bool check_f1[] = {
	false,  true, false,  // partials w.r.t x0 and (x0, x1, x2)
	true,  false, false,  // partials w.r.t x1 and (x0, x1, x2)
	false, false, false   // partials w.r.t x2 and (x0, x1, x2)
};

// define the template function BoolCases<Vector> in empty namespace
template <typename Vector> // vector class, elements of type bool
bool BoolCases(void)
{	bool ok = true;
	using CppAD::AD;

	// domain space vector
	size_t n = 3;
	CPPAD_TESTVECTOR(AD<double>) ax(n);
	ax[0] = 0.;
	ax[1] = 1.;
	ax[2] = 2.;

	// declare independent variables and start recording
	CppAD::Independent(ax);

	// range space vector
	size_t m = 2;
	CPPAD_TESTVECTOR(AD<double>) ay(m);
	ay[0] = sin( ax[2] );
	ay[1] = ax[0] * ax[1];

	// create f: x -> y and stop tape recording
	CppAD::ADFun<double> f(ax, ay);

	// sparsity pattern for the identity matrix
	Vector r(n * n);
	size_t i, j;
	for(i = 0; i < n; i++)
	{	for(j = 0; j < n; j++)
			r[ i * n + j ] = (i == j);
	}

	// compute sparsity pattern for J(x) = F^{(1)} (x)
	f.ForSparseJac(n, r);

	// compute sparsity pattern for H(x) = F_0^{(2)} (x)
	Vector s(m);
	for(i = 0; i < m; i++)
		s[i] = false;
	s[0] = true;
	Vector h(n * n);
	h    = f.RevSparseHes(n, s);

	// check values
	for(i = 0; i < n; i++)
		for(j = 0; j < n; j++)
			ok &= (h[ i * n + j ] == check_f0[ i * n + j ] );

	// compute sparsity pattern for H(x) = F_1^{(2)} (x)
	for(i = 0; i < m; i++)
		s[i] = false;
	s[1] = true;
	h    = f.RevSparseHes(n, s);

	// check values
	for(i = 0; i < n; i++)
		for(j = 0; j < n; j++)
			ok &= (h[ i * n + j ] == check_f1[ i * n + j ] );

	// call that transposed the result
	bool transpose = true;
	h    = f.RevSparseHes(n, s, transpose);

	// This h is symmetric, because R is symmetric, not really testing here
	for(i = 0; i < n; i++)
		for(j = 0; j < n; j++)
			ok &= (h[ j * n + i ] == check_f1[ i * n + j ] );

	return ok;
}
// define the template function SetCases<Vector> in empty namespace
template <typename Vector> // vector class, elements of type std::set<size_t>
bool SetCases(void)
{	bool ok = true;
	using CppAD::AD;

	// domain space vector
	size_t n = 3;
	CPPAD_TESTVECTOR(AD<double>) ax(n);
	ax[0] = 0.;
	ax[1] = 1.;
	ax[2] = 2.;

	// declare independent variables and start recording
	CppAD::Independent(ax);

	// range space vector
	size_t m = 2;
	CPPAD_TESTVECTOR(AD<double>) ay(m);
	ay[0] = sin( ax[2] );
	ay[1] = ax[0] * ax[1];

	// create f: x -> y and stop tape recording
	CppAD::ADFun<double> f(ax, ay);

	// sparsity pattern for the identity matrix
	Vector r(n);
	size_t i;
	for(i = 0; i < n; i++)
	{	assert( r[i].empty() );
		r[i].insert(i);
	}

	// compute sparsity pattern for J(x) = F^{(1)} (x)
	f.ForSparseJac(n, r);

	// compute sparsity pattern for H(x) = F_0^{(2)} (x)
	Vector s(1);
	assert( s[0].empty() );
	s[0].insert(0);
	Vector h(n);
	h    = f.RevSparseHes(n, s);

	// check values
	std::set<size_t>::iterator itr;
	size_t j;
	for(i = 0; i < n; i++)
	{	for(j = 0; j < n; j++)
		{	bool found = h[i].find(j) != h[i].end();
			ok        &= (found == check_f0[i * n + j]);
		}
	}

	// compute sparsity pattern for H(x) = F_1^{(2)} (x)
	s[0].clear();
	assert( s[0].empty() );
	s[0].insert(1);
	h    = f.RevSparseHes(n, s);

	// check values
	for(i = 0; i < n; i++)
	{	for(j = 0; j < n; j++)
		{	bool found = h[i].find(j) != h[i].end();
			ok        &= (found == check_f1[i * n + j]);
		}
	}

	// call that transposed the result
	bool transpose = true;
	h    = f.RevSparseHes(n, s, transpose);

	// This h is symmetric, because R is symmetric, not really testing here
	for(i = 0; i < n; i++)
	{	for(j = 0; j < n; j++)
		{	bool found = h[j].find(i) != h[j].end();
			ok        &= (found == check_f1[i * n + j]);
		}
	}

	return ok;
}
} // End empty namespace

# include <vector>
# include <valarray>
bool rev_sparse_hes(void)
{	bool ok = true;
	// Run with Vector equal to four different cases
	// all of which are Simple Vectors with elements of type bool.
	ok &= BoolCases< CppAD::vector  <bool> >();
	ok &= BoolCases< CppAD::vectorBool     >();
	ok &= BoolCases< std::vector    <bool> >();
	ok &= BoolCases< std::valarray  <bool> >();

	// Run with Vector equal to two different cases both of which are
	// Simple Vectors with elements of type std::set<size_t>
	typedef std::set<size_t> set;
	ok &= SetCases< CppAD::vector  <set> >();
	ok &= SetCases< std::vector    <set> >();

	// Do not use valarray because its element access in the const case
	// returns a copy instead of a reference
	// ok &= SetCases< std::valarray  <set> >();

	return ok;
}


// END C++
